Converting Mixed Numbers to Improper Fractions

Show your work for each problem.

1.
Which improper fraction is equal to $1\frac{1}{2}$ ?
1. a) $\frac{4}{2}$
2. b) $\frac{2}{2}$
3. c) $\frac{1}{2}$
4. d) $\frac{3}{2}$
Answer: $\frac{3}{2}$
$1 \times 2 + 1 = 3$ , so $1\frac{1}{2} = \frac{3}{2}$ : two halves in the whole plus one more half.
2.
Convert $2\frac{1}{4}$ to an improper fraction. Write it as a fraction, like 7/4.
Answer: 9/4
$2 \times 4 + 1 = 8 + 1 = 9$ , and the denominator stays $4$ . So $2\frac{1}{4}$ $= \frac{9}{4}$ .
3.
Convert $2\frac{3}{5}$ to an improper fraction step by step.
Answer: 13/5
1. Multiply the whole number by the denominator: $2 \times 5$ 10
2. Add the numerator. What is the new numerator? 13
3. What is the denominator of the improper fraction? 5
4.
What is the first step to convert $3\frac{2}{7}$ to an improper fraction?
1. a)Multiply $3$ by $7$
2. b)Add $3$ and $7$
3. c)Multiply $3$ by $2$
4. d)Add $3$ and $2$
Answer: Multiply $3$ by $7$
First multiply the whole number by the denominator: $3 \times 7 = 21$ . Then add the numerator: $21 + 2 = 23$ , so $\frac{23}{7}$ .
5.
Write $1\frac{2}{3}$ as an improper fraction. Write it as a fraction, like 7/4.
Answer: 5/3
$1 \times 3 + 2 = 3 + 2 = 5$ , and the denominator stays $3$ . So $1\frac{2}{3}$ $= \frac{5}{3}$ .
6.
Write the whole number $2$ as a fraction with denominator $3$ .
Answer: 6/3
1. $1 = \frac{?}{3}$ . What is the missing numerator? 3
2. $2 = \frac{?}{3}$ . What is the missing numerator? 6
7.
Which improper fraction is equal to $3\frac{4}{5}$ ?
1. a) $\frac{12}{5}$
2. b) $\frac{7}{5}$
3. c) $\frac{19}{5}$
4. d) $\frac{20}{5}$
Answer: $\frac{19}{5}$
$3 \times 5 + 4 = 15 + 4 = 19$ , so $3\frac{4}{5} = \frac{19}{5}$ . $\frac{12}{5}$ comes from $3 \times 4$ , $\frac{7}{5}$ from $3 + 4$ , and $\frac{20}{5}$ is $4$ wholes.
8.
Convert $4\frac{3}{8}$ to an improper fraction. Write it as a fraction, like 7/4.
Answer: 35/8
$4 \times 8 + 3 = 32 + 3 = 35$ , and the denominator stays $8$ . So $4\frac{3}{8}$ $= \frac{35}{8}$ .
9.
Convert $5\frac{2}{3}$ to an improper fraction step by step.
Answer: 17/3
1. Multiply the whole number by the denominator: $5 \times 3$ 15
2. Add the numerator. What is the new numerator? 17
3. What is the denominator of the improper fraction? 3
10.
Write the whole number $4$ as a fraction with denominator $5$ .
Answer: 20/5
1. $1 = \frac{?}{5}$ . What is the missing numerator? 5
2. $4 = \frac{?}{5}$ . What is the missing numerator? 20
11.
Mia converted $2\frac{3}{4}$ and got $\frac{5}{4}$ . What did she do wrong?
1. a)She multiplied $3$ by $4$
2. b)Nothing, her answer is correct
3. c)She changed the denominator
4. d)She added $2$ and $3$ instead of first multiplying $2$ by $4$
Answer: She added $2$ and $3$ instead of first multiplying $2$ by $4$
Mia did $2 + 3 = 5$ . She should first multiply $2 \times 4 = 8$ and then add $3$ : $8 + 3 = 11$ , so the answer is $\frac{11}{4}$ .
12.
A recipe uses $2\frac{1}{3}$ cups of milk. Your measuring cup holds $\frac{1}{3}$ cup. How many times do you fill it? Enter a whole number.
Answer: 7
$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$ , so you fill the cup $7$ times.
13.
Convert $3\frac{5}{6}$ to an improper fraction step by step.
Answer: 23/6
1. Multiply the whole number by the denominator: $3 \times 6$ 18
2. Add the numerator. What is the new numerator? 23
3. What is the denominator of the improper fraction? 6
14.
Which is greater: $2\frac{3}{5}$ or $\frac{12}{5}$ ?
1. a) $2\frac{3}{5}$
2. b)They are equal
3. c)They cannot be compared
4. d) $\frac{12}{5}$
Answer: $2\frac{3}{5}$
$2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5}$ . Since $13 > 12$ , $2\frac{3}{5}$ is greater than $\frac{12}{5}$ .
15.
Convert $7\frac{5}{9}$ to an improper fraction. Write it as a fraction, like 7/4.
Answer: 68/9
$7 \times 9 + 5 = 63 + 5 = 68$ , and the denominator stays $9$ . So $7\frac{5}{9}$ $= \frac{68}{9}$ .
16.
Convert $10\frac{3}{4}$ to an improper fraction step by step.
Answer: 43/4
1. Multiply the whole number by the denominator: $10 \times 4$ 40
2. Add the numerator. What is the new numerator? 43
3. What is the denominator of the improper fraction? 4
4. Check: how many whole times does $4$ go into $43$ ? 10
17.
A ribbon is $3\frac{2}{5}$ meters long. You cut it into pieces that are each $\frac{1}{5}$ meter long. How many pieces do you get?
Answer: 17
1. How many fifths of a meter are in $3$ whole meters? 15
2. Add the $2$ extra fifths. How many fifths in total? 17
3. How many pieces of $\frac{1}{5}$ meter do you get? 17
18.
Calculate $1\frac{1}{2} + 2\frac{1}{2}$ by first converting both mixed numbers to improper fractions.
Answer: 4
1. Write $1\frac{1}{2}$ as $\frac{?}{2}$ . What is the numerator? 3
2. Write $2\frac{1}{2}$ as $\frac{?}{2}$ . What is the numerator? 5
3. Add the halves: $\frac{3}{2} + \frac{5}{2} = \frac{?}{2}$ 8
4. Write $\frac{8}{2}$ as a whole number: 4